A novel approach in modeling the ionic transport in the electrolyte of Li-ion batteries is here resented. Diffusion and migration processes govern the transport of ions in solution in the absence of onvection. In the porous electrode theory  it is common to model these processes via mass balance equations and electroneutrality. A parabolic set of equations arises, in terms of a non constant electric field which is afflicted by the paradox of being generated without electrical charges. To remedy this contradiction, Maxwell's equations have been used here, coupled to Faraday's law of electrochemical charge transfer. The set of continuity equations for mass and Maxwell's equations lead to a consistent model, with distinctive energy characteristics. Numerical examples show the robustness of the approach, which is well suited for multi-scale analyses [2,3].